There are various types of strips, i.e. steel strip, copper strip and non-metal strip, and only steel strip is taken as an example in the following description. Generally speaking, the strip shape is expressed by section shape and flatness, while the section shape by strip crown. The strip crown is usually expressed by thickness difference between the thickness at the center of a strip and the thickness at the point 25 mm from the edge thereof, denoted by C.sub.H and C.sub.h in the present invention. The flatness is usually expressed by elongation difference along width direction, donated by .DELTA..epsilon. in the present invention.
In recent years, customers are making more and more rigorous demands on the section shape and the flatness of a steel strip, meanwhile, manufacturers are expecting to produce strips with even smaller or fixed crown so as to improve yield. Therefore, how to realize free control of the strip crown and the flatness becomes the key issue in rolling techniques. In addition, the measurement, especially real time measurement is the first problem to be settled as to controlling the strip shape in strip rolling.
A mathematical model used for measuring strip shape was given in the paper "Comparison of Various Crown-control Mills in Hot Rolling" written by H. Matsumoto, K. Nakajima and T. Yanai for the 6th International Steel Rolling Conference held in Dusseldorf, Germany in June, 1994, ##EQU1## where C.sub.H --entry crown; C.sub.h --exit crown;
C.sup.F.sub.H --vector entry crown; PA1 C--mechanical strip crown indicating algebraic summation of original crown of rolls, and roll crowns due to rolling forces, rolling bending forces, unevenly-distributed temperature along rolls and erosion; PA1 h--exit thickness; PA1 H--entry thickness; PA1 .eta.--heredity coefficient expressed by the ratio of entry crown C.sub.H to exit crown C.sub.h ; ##EQU2## (1-.eta.)--imprinting ratio indicating the efficiency coefficient of the mechanical strip crown; .xi.--shape disturbing coefficient reflecting the relation between change of crown ratio and the flatness; .DELTA..epsilon.--the strip flatness; i--pass No. PA1 .DELTA.h.sub.i --reduction, expressed as .DELTA.h.sub.i =H.sub.i -h.sub.i ; PA1 R.sup.1.sub.i --radius of roll flattening, expressed as ##EQU8## i--No. of a mill stand or a pass.
For a given mill and a strip of certain width, the strip crown and the flatness of any pass i can be obtained by using the entry thickness H, the exit thickness h, the heredity coefficient .eta. obtained by entering the exit thickness h and the strip width B against prior experimental plots, and the shape disturbing coefficient .xi. by entering .gamma. against prior experimental plots of this paper. .gamma. is obtained by computation of the exit thickness h, the strip width B and the roll diameter 2R .
However, in practice, it is rather difficult to obtain .eta. correctly, because .eta. is not only a quadratic function of strip width and thickness but also related to the parameters of both a piece to be rolled and a mill to be measured. For the same mill and a strip of certain specification, the heredity coefficient .eta..sub.i of each pass must be worked out so as to calculate the real time strip crown C.sub.h.sbsb.i and the flatness .DELTA..epsilon..sub.i by using equations (1) and (3). For instance, eight heredity coefficients .eta..sub.i have to be worked out for an 8-pass rolling mill, which will complicate the control of rolling and be much more costly.
Therefore, it is the object of the present invention to provide a method to measure strip shape and a method using the measuring method to control the same in the process of rolling, in which calculation can be dramatically simplified.